Climate won't blow out vents

[awmustang]

So I have experienced this issue on 2 trips. Both times were on longer drivers (more than an hour) and in rainy conditions. The car will become stuffy like there is no air movement. If you try to turn the fan up you can hear that it speeds up but no extra air comes out of the vents. It has a sound like something is blocking the vents. If you try to change where the air is coming from it doesn't do anything, though maybe the air comes out a bit more from the defroster vents, but dash vents and floor vents get no air movement.
Shutting off the car resolves this issue temporarily.
The first time it was on the trip home and then it was fine the next day.
The second time it happened on the outgoing trip. Then when coming back it was fine for a while, and then started to happen again. Eventually I stopped and left the car off for several minutes and then the car was fine for the rest of the 15 minute drive home.
It seems very specific to driving in rain for more than a short trip and as soon as the car if power cycled it resets so I can't really take it in because it will be working just fine. Anyone else experience anything like this? Any advice to get the dealer to look at it?

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